document.write( "Question 872039: The sum of the digits in a two digit number is 12. The new number obtained when the digits are reversed is 36 more than the original number. Find the original number. (Help, please I am so confused by this question. We are using two variables and two equations to solve.) \n" ); document.write( "

Algebra.Com's Answer #525941 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "First, a little background, so you can understand what's going on:\r\n" );
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document.write( "Two digit numbers are always equal to \r\n" );
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document.write( "10 times their first digit plus their second digit.\r\n" );
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document.write( "For instance,\r\n" );
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document.write( "23 has first digit 2 and second digit 3.  (10 times 2) plus 3 = 20+3 = 23\r\n" );
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document.write( "74 has first digit 7 and second digit 4.  (10 times 7) plus 4 = 70+4 = 74\r\n" );
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document.write( "11 has first digit 1 and second digit 1.  (10 times 1) plus 1 = 10+1 = 11\r\n" );
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document.write( "So in general:\r\n" );
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document.write( "\"FS\" has first digit F and second digit S.  (10 times F) plus S = 10F+S  \r\n" );
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document.write( "If you swap the dgits from \"FS\" to \"SF\",\r\n" );
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document.write( "\"SF\" has first digit S and second digit F.  (10 times S) plus F = 10S+F  \r\n" );
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document.write( "Now for the problem:\r\n" );
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document.write( "Let F = first digit and S = second digit. \r\n" );
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document.write( "So the number = 10F + S\r\n" );
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document.write( "When you swap (reverse) the digits, the new number is 10S + F \r\n" );
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\n" ); document.write( "The sum of the digits in a two digit number is 12.
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document.write( "So the first equation is this: \r\n" );
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document.write( "F + S = 12\r\n" );
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\n" ); document.write( "The new number obtained when the digits are reversed is 36 more than the original number.
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document.write( "So\r\n" );
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document.write( "  \r\n" );
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document.write( "So the second equation is\r\n" );
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document.write( "  \r\n" );
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document.write( "Let's simplify that:\r\n" );
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document.write( "and simplify it further by dividing through by 9\r\n" );
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document.write( "So you have this system of equations:\r\n" );
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document.write( "Using the second equation, substitute F+4 for S in the \r\n" );
document.write( "first equation F+S = 12\r\n" );
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document.write( "F+(F+4) = 12\r\n" );
document.write( "  F+F+4 = 12\r\n" );
document.write( "   2F+4 = 12\r\n" );
document.write( "     2F = 8\r\n" );
document.write( "      F = 4\r\n" );
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document.write( "Substitute 4 for F in S=F+4\r\n" );
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document.write( "S=4+4\r\n" );
document.write( "S=8\r\n" );
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document.write( "So the first digit F is 4 and the second digit S is 8\r\n" );
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document.write( "So the number is 48.\r\n" );
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document.write( "Now let's check:\r\n" );
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\n" ); document.write( "The sum of the digits in a two digit number, 48 is 12.
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document.write( "That checks because 4+8 = 12\r\n" );
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\n" ); document.write( "The new number obtained when the digits are reversed, which is 84,
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document.write( "That checks because 84 is 36 more than 48, because when 36 more than\r\n" );
document.write( "48 is 48+36 = 84.\r\n" );
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document.write( "So 48 is the correct answer.\r\n" );
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document.write( "[Your teacher probably uses t and u instead of F and S, and says \r\n" );
document.write( "\"tens digit\" instead of \"First digit\" and \"ones or units digit\" instead \r\n" );
document.write( "of second digit.]\r\n" );
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document.write( "Edwin

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